数学最新文献

{"title":"Density Estimation via Periodic Scaled Korobov Kernel Method with Exponential Decay Condition","authors":"Ziyang Ye, Haoyuan Tan, Xiaoqun Wang, Zhijian He","doi":"10.1137/25m1770370","DOIUrl":"https://doi.org/10.1137/25m1770370","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 64, Issue 5, Page 2100-2122, October 2026. <br/> Abstract. We propose the periodic scaled Korobov kernel (PSKK) method for nonparametric density estimation on [math]. By first wrapping the target density into a periodic version through modulo operation and subsequently applying kernel ridge regression in scaled Korobov spaces, we extend the kernel approach proposed by Kazashi and Nobile [SIAM J. Numer. Anal., 61 (2023), pp. 1080–1102] and eliminate its requirement for inherent periodicity of the density function. This key modification enables effective estimation of densities defined on unbounded domains. We establish rigorous mean integrated squared error (MISE) bounds, proving that for densities with smoothness of order [math] and exponential decay, our PSKK method achieves an [math] MISE convergence rate with an arbitrarily small [math]. While matching the convergence rate of the previous kernel approach, our method applies to nonperiodic distributions at the cost of stronger differentiability and exponential decay assumptions. Numerical experiments confirm the theoretical results and demonstrate a significant improvement over traditional kernel density estimation in large-sample regimes.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"33 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149152577","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Note on Local Polynomial Regression for Time Series in Banach Spaces","authors":"Florian Heinrichs","doi":"10.1111/jtsa.70033","DOIUrl":"https://doi.org/10.1111/jtsa.70033","url":null,"abstract":"<p>This work extends local polynomial regression to Banach space-valued time series for estimating smoothly varying means and their derivatives in non-stationary data. The asymptotic properties of both the standard and bias-reduced Jackknife estimators are analyzed under mild moment conditions, establishing their convergence rates. Simulation studies assess the finite sample performance of these estimators and compare them with the Nadaraya–Watson estimator. Additionally, the proposed methods are applied to smooth EEG recordings for reconstructing eye movements and to video analysis for detecting pedestrians and abandoned objects.</p>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"47 6","pages":"1124-1138"},"PeriodicalIF":1.2,"publicationDate":"2026-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/jtsa.70033","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176927","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Density Conditions for \u0000 \u0000 \u0000 \u0000 k\u0000 \u0000 \u0000 Vertex-Disjoint Triangles in Tripartite Graphs","authors":"Mingyang Guo,&nbsp;Klas Markström","doi":"10.1002/jgt.70079","DOIUrl":"https://doi.org/10.1002/jgt.70079","url":null,"abstract":"&lt;p&gt;Let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 \u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 \u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be positive integers such that &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 \u0000 &lt;mo&gt;≥&lt;/mo&gt;\u0000 \u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be a tripartite graph with parts &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;A&lt;/mi&gt;\u0000 \u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 \u0000 &lt;mi&gt;B&lt;/mi&gt;\u0000 \u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 \u0000 &lt;mi&gt;C&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; such that &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;∣&lt;/mo&gt;\u0000 \u0000 &lt;mi&gt;A&lt;/mi&gt;\u0000 \u0000 &lt;mo&gt;∣&lt;/mo&gt;\u0000 \u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 \u0000 &lt;mo&gt;∣&lt;/mo&gt;\u0000 \u0000 &lt;mi&gt;B&lt;/mi&gt;\u0000 \u0000 &lt;mo&gt;∣&lt;/mo&gt;\u0000 \u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 \u0000 &lt;mo&gt;∣&lt;/mo&gt;\u0000 \u0000 &lt;mi&gt;C&lt;/mi&gt;\u0000 \u0000 &lt;mo&gt;∣&lt;/mo&gt;\u0000 \u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 \u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. Denote the edge densities of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;[&lt;/mo&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;A&lt;/mi&gt;\u0000 \u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"113 4","pages":"634-649"},"PeriodicalIF":1.0,"publicationDate":"2026-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.70079","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149177137","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Chromatic Ramsey Numbers and Two-Color Turán Densities","authors":"Maria Axenovich,&nbsp;Simon Gaa,&nbsp;Dingyuan Liu","doi":"10.1002/jgt.70086","DOIUrl":"https://doi.org/10.1002/jgt.70086","url":null,"abstract":"&lt;p&gt;Given a graph &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, its 2-color Turán number &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mtext&gt;ex&lt;/mtext&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 \u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 \u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 \u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 \u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 \u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is the maximum number of edges in an &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-vertex graph, such that the edges can be colored with two colors avoiding a monochromatic copy of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. Let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;π&lt;/mi&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 \u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 \u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 \u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 \u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 \u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 \u0000 &lt;msub&gt;\u0000 &lt;mi&gt;lim&lt;/mi&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"113 4","pages":"663-676"},"PeriodicalIF":1.0,"publicationDate":"2026-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.70086","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149177157","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Nonparametric Inference of Conditional Expectile Functions in Large-Scale Time Series Data With Improved Efficiency","authors":"Feipeng Zhang,&nbsp;Ping-Shou Zhong","doi":"10.1111/jtsa.70021","DOIUrl":"10.1111/jtsa.70021","url":null,"abstract":"<p>Expectile is a coherent and elicitable law-invariant risk measure widely applied in risk management. Existing methods based on iteratively reweighted least squares (IWLS) are not computationally efficient for large-scale sample sizes. To overcome the issue, we develop a direct nonparametric conditional expectile function estimator by inverting the local polynomial estimator of the conditional loss-gain function. The proposed estimator is computationally friendly and stable without using iterative algorithms that require computation with large-scale data in each iteration. We establish the asymptotic distribution of the proposed estimator. We further show that the proposed estimator has a smaller variance than the existing IWLS estimator and a smaller mean square error in various scenarios. Simulations confirm the computational and statistical efficiency of the proposed method. We further apply the proposed methods to an S&amp;P500 data set to illustrate the computational time to estimate the conditional expectile-based value-at-risk (EVaR) and the precision in out-of-sample prediction.</p>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"47 6","pages":"1098-1112"},"PeriodicalIF":1.2,"publicationDate":"2026-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13564231/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148957209","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Block-Primitive Rank 3 \u0000 \u0000 \u0000 \u0000 t\u0000 \u0000 \u0000 -Designs With Sporadic or Alternating Socle","authors":"Suyun Ding,&nbsp;Xiaoqin Zhan","doi":"10.1002/jcd.70034","DOIUrl":"https://doi.org/10.1002/jcd.70034","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;In this paper, we classify nontrivial &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;v&lt;/mi&gt;\u0000 \u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 \u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 \u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 \u0000 &lt;mi&gt;λ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 \u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; designs with &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 \u0000 &lt;mo&gt;≥&lt;/mo&gt;\u0000 \u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;v&lt;/mi&gt;\u0000 \u0000 &lt;mo&gt;≥&lt;/mo&gt;\u0000 \u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 \u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; admitting an automorphism group that acts primitively with rank 3 on the block set, under the assumption that the socle is a sporadic simple group or an alternating group. We show that, apart from the known symmetric examples, the only possibilities are the 2-, 3-, and 4-designs associated with the Mathieu groups &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 \u0000 &lt;mn&gt;22&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 \u0000 &lt;mn&gt;23&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, together with a small number of 2-designs on &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;v&lt;/mi&gt;\u0000 \u0000 &lt;mo&gt;∈&lt;/","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"34 12","pages":"555-568"},"PeriodicalIF":0.8,"publicationDate":"2026-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149177295","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On Flag-Transitive 2-\u0000 \u0000 \u0000 \u0000 \u0000 (\u0000 \u0000 v\u0000 ,\u0000 k\u0000 ,\u0000 λ\u0000 \u0000 )\u0000 \u0000 \u0000 \u0000 Designs With \u0000 \u0000 \u0000 \u0000 λ\u0000 ≤\u0000 4","authors":"Yihui Li,&nbsp;Shenglin Zhou","doi":"10.1002/jcd.70033","DOIUrl":"https://doi.org/10.1002/jcd.70033","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;Let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;D&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be a non-trivial 2-&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;v&lt;/mi&gt;\u0000 \u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 \u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 \u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 \u0000 &lt;mi&gt;λ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 \u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; design with &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;λ&lt;/mi&gt;\u0000 \u0000 &lt;mo&gt;≤&lt;/mo&gt;\u0000 \u0000 &lt;mn&gt;4&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, admitting a flag-transitive automorphism group &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; which is also properly innately transitive on points. Then &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is of almost simple quotient type. As a corollary, we obtain that &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is innately transitive on points if and only if it is primitive when &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;λ&lt;/mi&gt;\u0000 \u0000 &lt;mo&gt;≤&lt;/mo&gt;\u0000 \u0000 &lt;mn&gt;3&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. And we proved that there exists a unique 2-&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;v&lt;/mi&gt;\u0000 \u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 \u0000 ","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"34 12","pages":"545-554"},"PeriodicalIF":0.8,"publicationDate":"2026-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149177592","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mode Meets Mean: A New Robust Volatility","authors":"Tao Wang","doi":"10.1111/jtsa.70022","DOIUrl":"https://doi.org/10.1111/jtsa.70022","url":null,"abstract":"<div>\u0000 \u0000 <p>Ullah and Wang (<i>Journal of Time Series Analysis</i>, 46 (4), 748–773) introduced a novel nonparametric estimator for the volatility function that leverages the mode to complement traditional mean-based volatility measures, thereby highlighting unique features of the data. In this paper, we extend their framework to estimate traditional mean volatility by proposing a new approach, termed <i>robust mode-oriented volatility</i>. Our method treats the bandwidth parameter associate with the kernel objective function as a constant rather than a shrinkage parameter, prioritizing robustness and efficiency while maintaining its foundation in the mode-based framework. We demonstrate that under <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>α</mi>\u0000 </mrow>\u0000 <annotation>$$ alpha $$</annotation>\u0000 </semantics></math>-mixing time series dependence, the proposed robust estimator retains the same asymptotic distribution as estimators derived under independence assumptions, while achieving the convergence rate of nonparametric mean regression. Furthermore, we theoretically establish that efficiency gains over traditional mean-based estimation can be realized by appropriately adjusting the bandwidth, particularly in the presence of outliers or heavy-tailed distributions. In contrast to Ullah and Wang (<i>Journal of Time Series Analysis</i>, 46 (4), 748–773), which focused on capturing volatility structures specific to the mode, our approach broadens the applicability of their framework by integrating it with traditional mean volatility estimation. The discussions on bandwidth selection and numerical examples highlight the finite sample performance and practical advantages of our robust estimation procedure.</p>\u0000 </div>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"47 6","pages":"1198-1205"},"PeriodicalIF":1.2,"publicationDate":"2026-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149177694","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stochastic Diffusion Driven by Internal and External Brownian Motions","authors":"Türker Özsarı","doi":"10.1111/sapm.70327","DOIUrl":"https://doi.org/10.1111/sapm.70327","url":null,"abstract":"<p>The purpose of this paper is to introduce a stochastic version of Fokas' unified transform formula for evolution PDEs on domains with boundary. The unified transform method, also known as Fokas method, was originally developed for deterministic initial-boundary value problems and has, so far, been used primarily in deterministic settings. The modifications introduced here lead to stochastic representation formulas that can be used to define mild solutions of stochastic initial-boundary value problems and to perform regularity analysis in rough fractional Sobolev spaces, below the algebra threshold. To present the main ideas, we consider the canonical model of linear and nonlinear diffusion equations with additive noise and stochastic boundary conditions in their most elementary form. We assume that the evolution is subject both to external forcing prescribed through Dirichlet-type Brownian motion and to internal additive forcing whose temporal component is also Brownian.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 4","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70327","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149205383","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Robust CDF-Filtering of a Location Parameter","authors":"Leopoldo Catania,&nbsp;Andrew C. Harvey,&nbsp;Alessandra Luati","doi":"10.1111/jtsa.70026","DOIUrl":"https://doi.org/10.1111/jtsa.70026","url":null,"abstract":"<p>This paper introduces a novel framework for designing robust filters associated with signal plus noise models having symmetric observation density. The filters are obtained by a recursion where the innovation term is a transform of the cumulative distribution function of the residuals. The latter downweights extreme values by construction and allows the filters to be analytically tractable. The updating scheme naturally arises as the solution of an optimization problem, where the objective function is a continuous version of the quantile check function, formerly employed as a proper scoring function for quantiles and used to construct robust minimum contrast estimators. Stationarity, ergodicity and invertibility are derived under minimal assumptions and preserved under different parametric specifications. Estimation is carried out by the method of maximum likelihood and the asymptotic theory is developed under misspecification. As an illustration, the new filters are applied to brain scan data and compared across Gaussian, Student-t, Cauchy and Logistic density specifications, with alternative methods. Additional results include a novel class of score-driven models and a subgaussian density suitable for robust filtering and modelling, arising as the infinite sum of independent non-identically distributed uniform random variables.</p>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"47 6","pages":"1113-1123"},"PeriodicalIF":1.2,"publicationDate":"2026-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/jtsa.70026","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149177286","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}